Slather jerk sauce on both sides of the venison and place on a hot grill. While the venison is cooking (about 3 minutes per side), saute onions in olive oil until translucent. After first turning the venison, place the halved rolls on the grill and toast until golden brown. Spread mayo on the rolls. Slice the venison thinly and put on the rolls, pile on the onions, and salt and pepper to taste.